CarLasso_Network(Removing DO_sat)

Introduction

This study explores connections between Bacteria and Archaea metagenome-assembled genomes (MAG) in lake and environmental parameters, analyzing raw count data from 16 bulk metagenomic samples. We applied a fraction method to pinpoint crucial MAGs and constructed a Bayesian sparse microbial network via a Gaussian chain graph (Carlasso) method to investigate their interactions among microbes and environmental influences on microbial composition. A comprehensive analysis of all MAGs further examined microbial community dynamics. Our approach revealed how specific MAGscorrelate with environmental variables(pH, water temperature, or dissolved oxygen, etc.) and uncover the microbiome’s complex interactions. We discovered some MAGs are only correlated with some environmental features, like dissolved oxygen saturation in percentage, within certain communities. Given Lake Mendota is anoxic for most of the summer, these insights are significant for understanding ecosystem dynamics.

Analysis 1

In our exploration of microbial diversity across temporal and spatial gradients, we utilize the fraction method to spotlight the “Top 10 OTUs with All Environmental Features.” This method selects OTUs based on their consistent presence over four months and across four depth levels.

Figure 1

library(CARlasso)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

set.seed(42)
changed_col<-read.csv("Network files/tax_10.csv")
changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
last_10_cols <- tail(names(changed_col), 10)
changed_col <- changed_col%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))
otu_res <- CARlasso(p__Proteobacteria_1+p__Verrucomicrobiota_2+p__Bacteroidota_3+p__Proteobacteria_4+p__Proteobacteria_5+p__Proteobacteria_6+ p__Verrucomicrobiota_7+p__Bacteroidota_8+p__Actinobacteriota_9+p__Proteobacteria_10~depth+wtemp_in_celsius+specific_conductivity+chlorophyll_RFU+phycocyanin_RFU+ Dissolved_organic_matter_RFU+Turbidity_RFU+DO_mg_L+PH, data = changed_col, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)


genomes_list <- c(
  'Ga0485157_metabat1.059',
  'Ga0485167_maxbin.109',
  'Ga0485162_maxbin.089',
  'Ga0485161_maxbin.110',
  'Ga0485161_maxbin.075',
  'Ga0485157_metabat1.036',
  'Ga0485165_metabat2_ours.012_sub',
  'Ga0485169_maxbin.201_sub',
  'Ga0485172_maxbin.081_sub',
  'Ga0485168_maxbin.153'
)

taxonomy_file_path = 'Fw_ lake mendota data/MAG_taxonomy.tsv'
taxonomy_df = read.csv(taxonomy_file_path, sep='\t')


t_count_file_path = 't_count_columnC.csv'
t_count_df = read.csv(t_count_file_path)
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)


phylum_names <- sapply(genomes_list, function(genome) genome_to_phylum_map[[genome]])
new_column_names <- paste(phylum_names, seq_along(genomes_list), sep="_")

reference_table <- data.frame(
  Original_Genome = genomes_list,
  Phylum_Level = new_column_names
)

plot(otu_res)

Network of Top10 OTUs with All Environmental Features

Table 1

print(reference_table)

##                    Original_Genome           Phylum_Level
## 1           Ga0485157_metabat1.059    p__Proteobacteria_1
## 2             Ga0485167_maxbin.109 p__Verrucomicrobiota_2
## 3             Ga0485162_maxbin.089      p__Bacteroidota_3
## 4             Ga0485161_maxbin.110    p__Proteobacteria_4
## 5             Ga0485161_maxbin.075    p__Proteobacteria_5
## 6           Ga0485157_metabat1.036    p__Proteobacteria_6
## 7  Ga0485165_metabat2_ours.012_sub p__Verrucomicrobiota_7
## 8         Ga0485169_maxbin.201_sub      p__Bacteroidota_8
## 9         Ga0485172_maxbin.081_sub  p__Actinobacteriota_9
## 10            Ga0485168_maxbin.153   p__Proteobacteria_10

Interpretation

Analysis 2

In this analysis, the fraction method was used again to pinpoint the “Top 15 OTUs with All Environmental Features,” based on their consistent presence over four months and across different depths, highlighting the primary persistent microorganisms in their respective ecosystems.

Figure 2

library(CARlasso)
set.seed(42)
changed_col<-read.csv("Network files/tax_15.csv")
changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
last_10_cols <- tail(names(changed_col), 10)
changed_col <- changed_col%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))
otu_res <- CARlasso(p__Proteobacteria_1+p__Verrucomicrobiota_2+p__Bacteroidota_3+p__Proteobacteria_4+p__Proteobacteria_5+p__Proteobacteria_6+ p__Verrucomicrobiota_7+p__Bacteroidota_8+p__Actinobacteriota_9+p__Proteobacteria_10+p__Proteobacteria_11+p__Actinobacteriota_12+p__Actinobacteriota_13+p__Verrucomicrobiota_14+p__Desulfobacterota_15~depth+wtemp_in_celsius+specific_conductivity+chlorophyll_RFU+phycocyanin_RFU+Dissolved_organic_matter_RFU+Turbidity_RFU+DO_mg_L+PH, data = changed_col, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)


genomes_list <- c(
  'Ga0485157_metabat1.059',
    'Ga0485167_maxbin.109',
    'Ga0485162_maxbin.089',
    'Ga0485161_maxbin.110',
    'Ga0485161_maxbin.075',
    'Ga0485157_metabat1.036',
    'Ga0485165_metabat2_ours.012_sub',
    'Ga0485169_maxbin.201_sub',
    'Ga0485172_maxbin.081_sub',
    'Ga0485168_maxbin.153',
    'Ga0485172_metabat2_ours.083',
    'Ga0485162_maxbin.023',
    'Ga0485160_maxbin.092',
    'Ga0485158_metabat2_jgi.024',
    'Ga0485162_metabat1.001'
)


phylum_names <- sapply(genomes_list, function(genome) genome_to_phylum_map[[genome]])
new_column_names <- paste(phylum_names, seq_along(genomes_list), sep="_")

reference_table <- data.frame(
  Original_Genome = genomes_list,
  Phylum_Level = new_column_names
)

plot(otu_res)

Table 2

print(reference_table)

##                    Original_Genome            Phylum_Level
## 1           Ga0485157_metabat1.059     p__Proteobacteria_1
## 2             Ga0485167_maxbin.109  p__Verrucomicrobiota_2
## 3             Ga0485162_maxbin.089       p__Bacteroidota_3
## 4             Ga0485161_maxbin.110     p__Proteobacteria_4
## 5             Ga0485161_maxbin.075     p__Proteobacteria_5
## 6           Ga0485157_metabat1.036     p__Proteobacteria_6
## 7  Ga0485165_metabat2_ours.012_sub  p__Verrucomicrobiota_7
## 8         Ga0485169_maxbin.201_sub       p__Bacteroidota_8
## 9         Ga0485172_maxbin.081_sub   p__Actinobacteriota_9
## 10            Ga0485168_maxbin.153    p__Proteobacteria_10
## 11     Ga0485172_metabat2_ours.083    p__Proteobacteria_11
## 12            Ga0485162_maxbin.023  p__Actinobacteriota_12
## 13            Ga0485160_maxbin.092  p__Actinobacteriota_13
## 14      Ga0485158_metabat2_jgi.024 p__Verrucomicrobiota_14
## 15          Ga0485162_metabat1.001  p__Desulfobacterota_15

Interpretation

Analysis 3

In our exploration of complex microbial ecosystems, understanding the intricate network of interactions among microbial taxa and their environment is crucial. To dissect this web of associations, we employed the SPIEC-EASI (SParse InversECovariance Estimation for Ecological Association Inference) algorithm—a sophisticated statistical tool designed for inferring ecological networks from microbial abundance data. The SPIEC-EASI method constructs a microbiome network by estimating sparse inverse covariance, providing insights into the potential interactions among different microbial taxa. For this, we consider the ‘betweenness’ centrality—a measure that captures the extent to which a node acts as a bridge along the shortest path between two other nodes. The “Top 15 Nodes for Betweenness with All Environmental Features” represents the most central species in a microbiome network. These are the species that often act as bridges or conduits for interactions between other species and environmental factors, signifying their pivotal roles within the ecological network.

Figure 3

library(CARlasso)
set.seed(42)
changed_col<-read.csv("Network files/tax_Betweenness.csv")
changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
last_10_cols <- tail(names(changed_col), 10)
changed_col <- changed_col%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))
otu_res <- CARlasso(p__Desulfobacterota_1
+p__Planctomycetota_2
+p__Proteobacteria_3
+p__Chloroflexota_4
+p__Bacteroidota_5
+p__Verrucomicrobiota_6
+p__Proteobacteria_7
+p__Actinobacteriota_8
+p__Krumholzibacteriota_9
+p__Armatimonadota_10
+p__Bacteroidota_11
+p__Verrucomicrobiota_12
+p__Actinobacteriota_13
+p__Firmicutes_A_14
+p__Desulfobacterota_15~depth+wtemp_in_celsius+specific_conductivity+chlorophyll_RFU+phycocyanin_RFU+Dissolved_organic_matter_RFU+Turbidity_RFU+DO_mg_L+PH, data = changed_col, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)


genomes_list <- c(
  "Ga0485158_maxbin.120_sub",
"Ga0485170_maxbin.090",
"Ga0485159_metabat1.040",
"Ga0485167_metabat2_ours.163",
"Ga0485166_metabat2_ours.038",
"Ga0485162_metabat2_ours.116",
"Ga0485162_metabat2_ours.050",
"Ga0485163_metabat1.181",
"Ga0485158_metabat2_ours.098",
"Ga0485169_metabat2_ours.035",
"Ga0485159_metabat2_ours.130_sub",
"Ga0485163_metabat1.115_sub",
"Ga0485159_maxbin.025",
"Ga0485161_metabat1.096",
"Ga0485167_metabat1.127_sub"
)


phylum_names <- sapply(genomes_list, function(genome) genome_to_phylum_map[[genome]])
new_column_names <- paste(phylum_names, seq_along(genomes_list), sep="_")

reference_table <- data.frame(
  Original_Genome = genomes_list,
  Phylum_Level = new_column_names
)

plot(otu_res)

Table 3

print(reference_table)

##                    Original_Genome             Phylum_Level
## 1         Ga0485158_maxbin.120_sub    p__Desulfobacterota_1
## 2             Ga0485170_maxbin.090     p__Planctomycetota_2
## 3           Ga0485159_metabat1.040      p__Proteobacteria_3
## 4      Ga0485167_metabat2_ours.163       p__Chloroflexota_4
## 5      Ga0485166_metabat2_ours.038        p__Bacteroidota_5
## 6      Ga0485162_metabat2_ours.116   p__Verrucomicrobiota_6
## 7      Ga0485162_metabat2_ours.050      p__Proteobacteria_7
## 8           Ga0485163_metabat1.181    p__Actinobacteriota_8
## 9      Ga0485158_metabat2_ours.098 p__Krumholzibacteriota_9
## 10     Ga0485169_metabat2_ours.035     p__Armatimonadota_10
## 11 Ga0485159_metabat2_ours.130_sub       p__Bacteroidota_11
## 12      Ga0485163_metabat1.115_sub  p__Verrucomicrobiota_12
## 13            Ga0485159_maxbin.025   p__Actinobacteriota_13
## 14          Ga0485161_metabat1.096       p__Firmicutes_A_14
## 15      Ga0485167_metabat1.127_sub   p__Desulfobacterota_15

Interpretation

Analysis 4

In this analysis, we focus on the “Top 15 Nodes for Closeness with All Environmental Features” within a microbial network. Closeness centrality measures how close a node is to all other nodes in the network, highlighting those that can rapidly interact or influence others. This measure provides insight into how efficiently information or material might spread from one node to the rest of the network.

Figure 4

library(CARlasso)
set.seed(42)
changed_col<-read.csv("Network files/tax_Closeness.csv")
changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
last_10_cols <- tail(names(changed_col), 10)
changed_col <- changed_col%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))
otu_res <- CARlasso(p__Verrucomicrobiota_1+p__Actinobacteriota_2
+p__Bacteroidota_3
+p__Bacteroidota_4
+p__Bacteroidota_5
+p__Actinobacteriota_6
+p__Bacteroidota_7
+p__Bacteroidota_8
+p__Actinobacteriota_9
+p__Proteobacteria_10
+p__Planctomycetota_11
+p__Proteobacteria_12
+p__Proteobacteria_13
+p__Bacteroidota_14
+p__Verrucomicrobiota_15~depth+wtemp_in_celsius+specific_conductivity+chlorophyll_RFU+phycocyanin_RFU+Dissolved_organic_matter_RFU+Turbidity_RFU+DO_mg_L+PH, data = changed_col, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)


genomes_list <- c(
  "Ga0485157_metabat1.069",
"Ga0485157_metabat2_ours.025",
"Ga0485157_metabat2_ours.091",
"Ga0485158_metabat2_ours.184",
"Ga0485159_maxbin.015",
"Ga0485160_maxbin.155_sub",
"Ga0485160_metabat2_ours.051",
"Ga0485160_metabat2_ours.071",
"Ga0485161_metabat1.109_sub",
"Ga0485162_metabat2_ours.036",
"Ga0485163_maxbin.002_sub",
"Ga0485163_maxbin.104_sub",
"Ga0485163_maxbin.129",
"Ga0485163_maxbin.130_sub",
"Ga0485163_maxbin.183_sub"
)


phylum_names <- sapply(genomes_list, function(genome) genome_to_phylum_map[[genome]])
new_column_names <- paste(phylum_names, seq_along(genomes_list), sep="_")

reference_table <- data.frame(
  Original_Genome = genomes_list,
  Phylum_Level = new_column_names
)

plot(otu_res)

Table 4

print(reference_table)

##                Original_Genome            Phylum_Level
## 1       Ga0485157_metabat1.069  p__Verrucomicrobiota_1
## 2  Ga0485157_metabat2_ours.025   p__Actinobacteriota_2
## 3  Ga0485157_metabat2_ours.091       p__Bacteroidota_3
## 4  Ga0485158_metabat2_ours.184       p__Bacteroidota_4
## 5         Ga0485159_maxbin.015       p__Bacteroidota_5
## 6     Ga0485160_maxbin.155_sub   p__Actinobacteriota_6
## 7  Ga0485160_metabat2_ours.051       p__Bacteroidota_7
## 8  Ga0485160_metabat2_ours.071       p__Bacteroidota_8
## 9   Ga0485161_metabat1.109_sub   p__Actinobacteriota_9
## 10 Ga0485162_metabat2_ours.036    p__Proteobacteria_10
## 11    Ga0485163_maxbin.002_sub   p__Planctomycetota_11
## 12    Ga0485163_maxbin.104_sub    p__Proteobacteria_12
## 13        Ga0485163_maxbin.129    p__Proteobacteria_13
## 14    Ga0485163_maxbin.130_sub      p__Bacteroidota_14
## 15    Ga0485163_maxbin.183_sub p__Verrucomicrobiota_15

Interpretation

Analysis 5

In the “Top 15 Nodes for PageRank with All Environmental Features” analysis, we apply the PageRank algorithm, originally designed to rank web pages, to assess the significance of OTUs within a microbiome network. This method evaluates the nodes not just by their direct connections, but also by the importance of their neighbors within the network. By focusing on PageRank centrality, we can identify OTUs that are deemed most ‘influential’ based on the network’s topology, providing a nuanced view of which species are vital in the ecological context and how they might affect or be affected by various environmental features.

Figure 5

library(CARlasso)
set.seed(42)
changed_col<-read.csv("Network files/tax_Page_Rank.csv")
changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
last_10_cols <- tail(names(changed_col), 10)
changed_col <- changed_col%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))
otu_res <- CARlasso(p__Krumholzibacteriota_1
+p__Bacteroidota_2
+p__Verrucomicrobiota_3
+p__Planctomycetota_4
+p__Verrucomicrobiota_5
+p__Planctomycetota_6
+p__Proteobacteria_7
+p__Proteobacteria_8
+p__Bacteroidota_9
+p__Bacteroidota_10
+p__Bacteroidota_11
+p__Actinobacteriota_12
+p__Verrucomicrobiota_13
+p__Proteobacteria_14
+p__Planctomycetota_15~depth+wtemp_in_celsius+specific_conductivity+chlorophyll_RFU+phycocyanin_RFU+Dissolved_organic_matter_RFU+Turbidity_RFU+DO_mg_L+PH, data = changed_col, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)


genomes_list <- c(
  "Ga0485158_metabat2_ours.098",
"Ga0485166_metabat2_ours.038",
"Ga0485167_metabat2_ours.023",
"Ga0485170_maxbin.090",
"Ga0485161_metabat2_ours.167_sub",
"Ga0485171_maxbin.130_sub",
"Ga0485161_maxbin.110",
"Ga0485164_metabat2_ours.069_sub",
"Ga0485171_metabat1.063",
"Ga0485159_metabat2_ours.079",
"Ga0485171_metabat2_ours.127_sub",
"Ga0485159_metabat2_ours.155_sub",
"Ga0485158_metabat1.076",
"Ga0485171_metabat1.030",
"Ga0485168_metabat2_ours.135_sub"

)


phylum_names <- sapply(genomes_list, function(genome) genome_to_phylum_map[[genome]])
new_column_names <- paste(phylum_names, seq_along(genomes_list), sep="_")

reference_table <- data.frame(
  Original_Genome = genomes_list,
  Phylum_Level = new_column_names
)

plot(otu_res)

Table 5

print(reference_table)# The table Below serves as a reference to the response nodes in the plot!

##                    Original_Genome             Phylum_Level
## 1      Ga0485158_metabat2_ours.098 p__Krumholzibacteriota_1
## 2      Ga0485166_metabat2_ours.038        p__Bacteroidota_2
## 3      Ga0485167_metabat2_ours.023   p__Verrucomicrobiota_3
## 4             Ga0485170_maxbin.090     p__Planctomycetota_4
## 5  Ga0485161_metabat2_ours.167_sub   p__Verrucomicrobiota_5
## 6         Ga0485171_maxbin.130_sub     p__Planctomycetota_6
## 7             Ga0485161_maxbin.110      p__Proteobacteria_7
## 8  Ga0485164_metabat2_ours.069_sub      p__Proteobacteria_8
## 9           Ga0485171_metabat1.063        p__Bacteroidota_9
## 10     Ga0485159_metabat2_ours.079       p__Bacteroidota_10
## 11 Ga0485171_metabat2_ours.127_sub       p__Bacteroidota_11
## 12 Ga0485159_metabat2_ours.155_sub   p__Actinobacteriota_12
## 13          Ga0485158_metabat1.076  p__Verrucomicrobiota_13
## 14          Ga0485171_metabat1.030     p__Proteobacteria_14
## 15 Ga0485168_metabat2_ours.135_sub    p__Planctomycetota_15

Interpretation

Analysis 6

Our analysis centers on the “Top 15 Nodes for Degree with All Environmental Features” within a microbial network. Degree centrality focuses on the number of direct connections, or edges, that a node has. In this context, we identify and examine the OTUs that exhibit the highest degree of connectivity, reflecting their active engagement with other microbes and environmental parameters. Such nodes are considered highly interactive within the network, potentially playing crucial roles in microbial processes and environmental interactions. This analysis aims to uncover which OTUs are the most connected and thus may have a significant impact on the structure and function of their ecological community.

Figure 6

library(CARlasso)

set.seed(42)
changed_col<-read.csv("Network files/tax_Degree.csv")
changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
last_10_cols <- tail(names(changed_col), 10)
changed_col <- changed_col%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))

otu_res <- CARlasso(p__Krumholzibacteriota_1
+p__Bacteroidota_2
+p__Bacteroidota_3
+p__Proteobacteria_4
+p__Planctomycetota_5
+p__Bacteroidota_6
+p__Chloroflexota_7
+p__Bacteroidota_8
+p__Verrucomicrobiota_9
+p__Actinobacteriota_10
+p__Planctomycetota_11
+p__Chloroflexota_12
+p__Proteobacteria_13
+p__Firmicutes_A_14
+p__Verrucomicrobiota_15~depth+wtemp_in_celsius+specific_conductivity+chlorophyll_RFU+phycocyanin_RFU+Dissolved_organic_matter_RFU+Turbidity_RFU+DO_mg_L+PH, data = changed_col, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)


genomes_list <- c(
  "Ga0485158_metabat2_ours.098",
"Ga0485159_metabat2_ours.079",
"Ga0485171_metabat2_ours.127_sub",
"Ga0485171_metabat2_ours.004",
"Ga0485170_maxbin.090",
"Ga0485171_metabat1.063",
"Ga0485157_metabat2_ours.019",
"Ga0485166_metabat2_ours.038",
"Ga0485167_metabat2_ours.023",
"Ga0485170_maxbin.059_sub",
"Ga0485171_maxbin.130_sub",
"Ga0485160_metabat2_ours.158_sub",
"Ga0485161_maxbin.110",
"Ga0485161_metabat1.096",
"Ga0485161_metabat2_ours.167_sub"

)


phylum_names <- sapply(genomes_list, function(genome) genome_to_phylum_map[[genome]])
new_column_names <- paste(phylum_names, seq_along(genomes_list), sep="_")

reference_table <- data.frame(
  Original_Genome = genomes_list,
  Phylum_Level = new_column_names
)

plot(otu_res)

Table 6

print(reference_table)

##                    Original_Genome             Phylum_Level
## 1      Ga0485158_metabat2_ours.098 p__Krumholzibacteriota_1
## 2      Ga0485159_metabat2_ours.079        p__Bacteroidota_2
## 3  Ga0485171_metabat2_ours.127_sub        p__Bacteroidota_3
## 4      Ga0485171_metabat2_ours.004      p__Proteobacteria_4
## 5             Ga0485170_maxbin.090     p__Planctomycetota_5
## 6           Ga0485171_metabat1.063        p__Bacteroidota_6
## 7      Ga0485157_metabat2_ours.019       p__Chloroflexota_7
## 8      Ga0485166_metabat2_ours.038        p__Bacteroidota_8
## 9      Ga0485167_metabat2_ours.023   p__Verrucomicrobiota_9
## 10        Ga0485170_maxbin.059_sub   p__Actinobacteriota_10
## 11        Ga0485171_maxbin.130_sub    p__Planctomycetota_11
## 12 Ga0485160_metabat2_ours.158_sub      p__Chloroflexota_12
## 13            Ga0485161_maxbin.110     p__Proteobacteria_13
## 14          Ga0485161_metabat1.096       p__Firmicutes_A_14
## 15 Ga0485161_metabat2_ours.167_sub  p__Verrucomicrobiota_15

Interpretation

The MAG Ga0485171_metabat1.063 (p__Bacteroidota_6) exhibits a strong correlation with environmental attributes such as depth, water temperature, specific conductivity, chlorophyll RFU, phycocyanin RFU, dissolved oxygen (DO) in mg/L, and PH.

Analysis 7

Since the network can not be build on the intersection, this analysis is being skipped.

Analysis 8(Starting with Permutation)

In Analysis 8, we delve into the structural significance of the OTU p__Bacteroidota_3 (Ga0485162_maxbin.089) within our microbial network. Recognized for its pivotal role, this genome will undergo a permutation analysis alongside nine other randomly selected OTUs. By systematically substituting this key node with other OTUs and observing the resultant changes in network dynamics, we aim to quantify the impact of p__Bacteroidota_3 on the network’s integrity and functionality.

if (!requireNamespace("readr", quietly = TRUE)) install.packages("readr")
if (!requireNamespace("dplyr", quietly = TRUE)) install.packages("dplyr")
library(readr)

## Warning: package 'readr' was built under R version 4.3.1

library(dplyr)
taxonomy_file_path <- 'Fw_ lake mendota data/MAG_taxonomy.tsv'
taxonomy_df <- read_tsv(taxonomy_file_path)

## Rows: 431 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (8): Genome, Domain, Phylum, Class, Order, Family, Genus, Species
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

t_count_file_path <- 't_count_columnC.csv'
t_count_df <- read_csv(t_count_file_path)

## Rows: 16 Columns: 442
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (1): Sample
## dbl (441): Ga0485157_maxbin.014, Ga0485157_maxbin.074_sub, Ga0485157_maxbin....
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Create a mapping of genomes to phylum
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)

# Define your specific genomes list
genomes_list <- c(
  "Ga0485159_maxbin.004_sub", "Ga0485169_maxbin.078", 'Ga0485162_maxbin.089',
  "Ga0485162_metabat2_ours.126", "Ga0485159_metabat2_ours.129_sub",
  "Ga0485163_metabat2_ours.245_sub", "Ga0485162_metabat2_ours.040",
  "Ga0485160_metabat2_ours.184_sub", "Ga0485172_metabat2_ours.152",
  "Ga0485161_metabat1.096"
)

new_column_names_list <- vector("list", length(genomes_list))
names(new_column_names_list) <- genomes_list

# Reset sequence number in case it's being reused
seq_num <- 1

for (i in seq_along(genomes_list)) {
  genome <- genomes_list[i]
  phylum <- genome_to_phylum_map[genome]
  
  # Specific assignment for 'Ga0485162_maxbin.089' to ensure it gets _3
  if (genome == 'Ga0485162_maxbin.089') {
    assign_num <- 3
  } else {
    # Skip over 3 if it's already been assigned
    if (seq_num == 3) {
      seq_num <- 4
    }
    assign_num <- seq_num
    seq_num <- seq_num + 1
  }
  
  if (!is.null(phylum) && genome %in% colnames(t_count_df)) {
    new_column_name <- paste(phylum, assign_num, sep = "_") # Append underscore and sequence number
    # Append the new column name to the list in order
    new_column_names_list[[genome]] <- new_column_name
    
    # Rename the column in t_count_df
    if (genome %in% colnames(t_count_df)) {
      colnames(t_count_df)[colnames(t_count_df) == genome] <- new_column_name
    }
  }
}

# Remove NULL entries if any genome was not found in t_count_df
new_column_names_list <- new_column_names_list[!sapply(new_column_names_list, is.null)]

# Display the first few rows of the modified DataFrame to verify changes
#print(head(t_count_df))

Figure 8

library(CARlasso)
set.seed(42)
t_count_df$DO_mg_L <- ifelse(t_count_df$DO_mg_L < 0, 0, t_count_df$DO_mg_L)
last_10_cols <- tail(names(t_count_df), 10)
t_count_df <- t_count_df%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))

new_column_names_list <- as.character(new_column_names_list)
sequence_numbers <- sapply(strsplit(new_column_names_list, "_"), function(x) as.numeric(tail(x, 1)))

# Create a named vector with names as original column names and values as extracted sequence numbers
named_sequences <- setNames(sequence_numbers, new_column_names_list)
# Sort the named vector by sequence numbers to get the names (original column names) in the correct order
ordered_names <- names(sort(named_sequences))
# Construct the predictor part of the formula with column names in the correct order based on sequence numbers
predictor_formula_part <- paste(ordered_names, collapse = " + ")
# Construct the full formula by appending the response variables and predictors
full_formula <- as.formula(paste(predictor_formula_part,"~", "depth + wtemp_in_celsius + specific_conductivity + chlorophyll_RFU + phycocyanin_RFU + Dissolved_organic_matter_RFU + Turbidity_RFU + DO_mg_L + PH "))
 otu_res <- CARlasso(full_formula, data = t_count_df, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)
plot(otu_res)

reference_table <- data.frame(
  Original_Genome = genomes_list,  
  Phylum_Levels= ordered_names  
)

Table 8

print(reference_table)

##                    Original_Genome         Phylum_Levels
## 1         Ga0485159_maxbin.004_sub    p__Cyanobacteria_1
## 2             Ga0485169_maxbin.078   p__Proteobacteria_2
## 3             Ga0485162_maxbin.089     p__Bacteroidota_3
## 4      Ga0485162_metabat2_ours.126   p__Proteobacteria_4
## 5  Ga0485159_metabat2_ours.129_sub    p__Cyanobacteria_5
## 6  Ga0485163_metabat2_ours.245_sub  p__Planctomycetota_6
## 7      Ga0485162_metabat2_ours.040   p__Proteobacteria_7
## 8  Ga0485160_metabat2_ours.184_sub    p__Cyanobacteria_8
## 9      Ga0485172_metabat2_ours.152 p__Actinobacteriota_9
## 10          Ga0485161_metabat1.096    p__Firmicutes_A_10

Interpretation

Analysis 9

In this analysis, we concentrate on the OTU p__Desulfobacterota_15(Ga0485162_metabat1.001), distinguished for its significant connections with environmental features as revealed in Analysis 2. Recognizing its critical interactions, we opt to retain this genome while permuting it alongside 14 other randomly selected OTUs within our microbial network.

data <- read_csv("Fw_ lake mendota data/coverm_431_MAGS_metagenomes_reads_count.csv")

## Rows: 431 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Genome
## dbl (16): 2020-10-19_23.5m, 2020-10-08_15m, 2020-10-19_15m, 2020-09-11_15m, ...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

data_t <- t(data)
data_df <- as.data.frame(data_t)
colnames(data_df) <- data_df[1, ]
data_df <- data_df[-1, ]

excluded_columns <- c('Ga0485157_metabat1.059',
    'Ga0485167_maxbin.109',
    'Ga0485162_maxbin.089',
    'Ga0485161_maxbin.110',
    'Ga0485161_maxbin.075',
    'Ga0485157_metabat1.036',
    'Ga0485165_metabat2_ours.012_sub',
    'Ga0485169_maxbin.201_sub',
    'Ga0485172_maxbin.081_sub',
    'Ga0485168_maxbin.153',
    'Ga0485172_metabat2_ours.083',
    'Ga0485162_maxbin.023',
    'Ga0485160_maxbin.092',
    'Ga0485158_metabat2_jgi.024',
    'Ga0485162_metabat1.001')

set.seed(42)
available_columns <- setdiff(colnames(data_df), excluded_columns)
random_column_names <- sample(available_columns, 14)
taxonomy_file_path <- 'Fw_ lake mendota data/MAG_taxonomy.tsv'
taxonomy_df <- read_tsv(taxonomy_file_path)

## Rows: 431 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (8): Genome, Domain, Phylum, Class, Order, Family, Genus, Species
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

t_count_file_path <- 't_count_columnC.csv'
t_count_df <- read_csv(t_count_file_path)

## Rows: 16 Columns: 442
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (1): Sample
## dbl (441): Ga0485157_maxbin.014, Ga0485157_maxbin.074_sub, Ga0485157_maxbin....
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Create a mapping of genomes to phylum
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)

# Define your specific genomes list
genomes_list <- c(
  "Ga0485159_maxbin.015","Ga0485169_maxbin.202","Ga0485163_maxbin.015_sub","Ga0485159_metabat2_ours.130_sub", "Ga0485164_metabat2_jgi.001", "Ga0485162_metabat2_ours.100_sub","Ga0485161_maxbin.064","Ga0485172_metabat2_ours.152"  ,"Ga0485161_metabat2_jgi.003_sub", "Ga0485168_metabat2_ours.036"    
,"Ga0485157_metabat2_ours.077", "Ga0485169_metabat1.104","Ga0485169_metabat2_ours.239", "Ga0485160_metabat1.067","Ga0485162_metabat1.001"
)

new_column_names_list <- vector("list", length(genomes_list))
names(new_column_names_list) <- genomes_list

seq_num <- 1

for (genome in genomes_list) {
  phylum <- genome_to_phylum_map[genome]
  
  if (!is.null(phylum) && genome %in% colnames(t_count_df)) {
    # Construct the new column name using the phylum and the current sequence number
    new_column_name <- paste(phylum, seq_num, sep = "_")
    
    # Update the list with the new column name
    new_column_names_list[genome] <- new_column_name
    
    # Rename the column in t_count_df
    colnames(t_count_df)[colnames(t_count_df) == genome] <- new_column_name
    
    # Increment the sequence number for the next iteration
    seq_num <- seq_num + 1
  }
}

# Display the first few rows of the modified DataFrame to verify changes
#print(head(t_count_df))
#print(new_column_names_list)

Figure 9

library(CARlasso)
set.seed(42)
t_count_df$DO_mg_L <- ifelse(t_count_df$DO_mg_L < 0, 0, t_count_df$DO_mg_L)
last_10_cols <- tail(names(t_count_df), 10)
t_count_df <- t_count_df%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))

predictor_formula_part <- paste(new_column_names_list, collapse = " + ")
# Construct the full formula by appending the response variables and predictors
full_formula <- as.formula(paste(predictor_formula_part,"~", "depth + wtemp_in_celsius + specific_conductivity + chlorophyll_RFU + phycocyanin_RFU + Dissolved_organic_matter_RFU + Turbidity_RFU +DO_mg_L + PH "))
 otu_res <- CARlasso(full_formula, data = t_count_df, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

  otu_res <- horseshoe(otu_res)
 plot(otu_res)

 phylum_levels_vector <- unlist(new_column_names_list)

# Create the reference table with genomes_list and the flattened phylum_levels_vector
reference_table <- data.frame(
  Original_Genome = names(phylum_levels_vector),  
  Phylum_Levels = phylum_levels_vector,
  stringsAsFactors = FALSE,  # Ensuring character data does not convert to factors
  row.names = NULL 
)

Table 9

print(reference_table)

##                    Original_Genome          Phylum_Levels
## 1             Ga0485159_maxbin.015      p__Bacteroidota_1
## 2             Ga0485169_maxbin.202      p__Bacteroidota_2
## 3         Ga0485163_maxbin.015_sub  p__Actinobacteriota_3
## 4  Ga0485159_metabat2_ours.130_sub      p__Bacteroidota_4
## 5       Ga0485164_metabat2_jgi.001    p__Proteobacteria_5
## 6  Ga0485162_metabat2_ours.100_sub    p__Proteobacteria_6
## 7             Ga0485161_maxbin.064  p__Actinobacteriota_7
## 8      Ga0485172_metabat2_ours.152  p__Actinobacteriota_8
## 9   Ga0485161_metabat2_jgi.003_sub p__Verrucomicrobiota_9
## 10     Ga0485168_metabat2_ours.036 p__Actinobacteriota_10
## 11     Ga0485157_metabat2_ours.077 p__Campylobacterota_11
## 12          Ga0485169_metabat1.104      p__Myxococcota_12
## 13     Ga0485169_metabat2_ours.239     p__Bacteroidota_13
## 14          Ga0485160_metabat1.067 p__Bdellovibrionota_14
## 15          Ga0485162_metabat1.001 p__Desulfobacterota_15

Interpretation

Analysis 10

In this study, we turn our attention to the genome p__Verrucomicrobiota_15(Ga0485163_maxbin.183_sub), a key player within our microbial network as identified by its closeness centrality measures. This genome stands out due to its pivotal connections across the network. To delve deeper into its role and the network’s resilience, we conduct a permutation analysis, where p__Bacteroidota_14 is alternated with 14 other randomly selected OTUs.

data <- read_csv("Fw_ lake mendota data/coverm_431_MAGS_metagenomes_reads_count.csv")

## Rows: 431 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Genome
## dbl (16): 2020-10-19_23.5m, 2020-10-08_15m, 2020-10-19_15m, 2020-09-11_15m, ...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

data_t <- t(data)
data_df <- as.data.frame(data_t)
colnames(data_df) <- data_df[1, ]
data_df <- data_df[-1, ]

excluded_columns <- c("Ga0485157_metabat1.069",
"Ga0485157_metabat2_ours.025",
"Ga0485157_metabat2_ours.091",
"Ga0485158_metabat2_ours.184",
"Ga0485159_maxbin.015",
"Ga0485160_maxbin.155_sub",
"Ga0485160_metabat2_ours.051",
"Ga0485160_metabat2_ours.071",
"Ga0485161_metabat1.109_sub",
"Ga0485162_metabat2_ours.036",
"Ga0485163_maxbin.002_sub",
"Ga0485163_maxbin.104_sub",
"Ga0485163_maxbin.129",
"Ga0485163_maxbin.130_sub",
"Ga0485163_maxbin.183_sub")

set.seed(42)
available_columns <- setdiff(colnames(data_df), excluded_columns)
random_column_names <- sample(available_columns, 14)
taxonomy_file_path <- 'Fw_ lake mendota data/MAG_taxonomy.tsv'
taxonomy_df <- read_tsv(taxonomy_file_path)

## Rows: 431 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (8): Genome, Domain, Phylum, Class, Order, Family, Genus, Species
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

t_count_file_path <- 't_count_columnC.csv'
t_count_df <- read_csv(t_count_file_path)

## Rows: 16 Columns: 442
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (1): Sample
## dbl (441): Ga0485157_maxbin.014, Ga0485157_maxbin.074_sub, Ga0485157_maxbin....
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Create a mapping of genomes to phylum
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)

# Define your specific genomes list
genomes_list <- c(
  "Ga0485159_maxbin.027","Ga0485169_maxbin.226_sub","Ga0485163_maxbin.041_sub","Ga0485159_metabat2_ours.135_sub","Ga0485165_metabat1.064_sub","Ga0485162_metabat2_ours.116","Ga0485161_metabat1.011","Ga0485172_metabat2_ours.152","Ga0485161_metabat2_ours.019_sub","Ga0485168_metabat2_ours.050_sub","Ga0485157_metabat2_ours.077","Ga0485169_metabat1.187_sub","Ga0485169_metabat2_ours.242", "Ga0485160_metabat1.086","Ga0485163_maxbin.183_sub"
)

new_column_names_list <- vector("list", length(genomes_list))
names(new_column_names_list) <- genomes_list

seq_num <- 1

for (genome in genomes_list) {
  phylum <- genome_to_phylum_map[genome]
  
  if (!is.null(phylum) && genome %in% colnames(t_count_df)) {
    # Construct the new column name using the phylum and the current sequence number
    new_column_name <- paste(phylum, seq_num, sep = "_")
    
    # Update the list with the new column name
    new_column_names_list[genome] <- new_column_name
    
    # Rename the column in t_count_df
    colnames(t_count_df)[colnames(t_count_df) == genome] <- new_column_name
    
    # Increment the sequence number for the next iteration
    seq_num <- seq_num + 1
  }
}

# Display the first few rows of the modified DataFrame to verify changes
#print(head(t_count_df))
#print(new_column_names_list)

Figure 10

library(CARlasso)
set.seed(42)
t_count_df$DO_mg_L <- ifelse(t_count_df$DO_mg_L < 0, 0, t_count_df$DO_mg_L)
last_10_cols <- tail(names(t_count_df), 10)
t_count_df <- t_count_df%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))

predictor_formula_part <- paste(new_column_names_list, collapse = " + ")
# Construct the full formula by appending the response variables and predictors
full_formula <- as.formula(paste(predictor_formula_part,"~", "depth + wtemp_in_celsius + specific_conductivity + chlorophyll_RFU + phycocyanin_RFU + Dissolved_organic_matter_RFU + Turbidity_RFU + DO_mg_L + PH "))
 otu_res <- CARlasso(full_formula, data = t_count_df, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

otu_res <- horseshoe(otu_res)
plot(otu_res)

phylum_levels_vector <- unlist(new_column_names_list)

# Create the reference table with genomes_list and the flattened phylum_levels_vector
reference_table <- data.frame(
  Original_Genome = names(phylum_levels_vector),  
  Phylum_Levels = phylum_levels_vector,
  stringsAsFactors = FALSE,  # Ensuring character data does not convert to factors
  row.names = NULL 
)

Table 10

print(reference_table)

##                    Original_Genome           Phylum_Levels
## 1             Ga0485159_maxbin.027      p__Cyanobacteria_1
## 2         Ga0485169_maxbin.226_sub  p__Verrucomicrobiota_2
## 3         Ga0485163_maxbin.041_sub     p__Proteobacteria_3
## 4  Ga0485159_metabat2_ours.135_sub    p__Planctomycetota_4
## 5       Ga0485165_metabat1.064_sub       p__Bacteroidota_5
## 6      Ga0485162_metabat2_ours.116  p__Verrucomicrobiota_6
## 7           Ga0485161_metabat1.011   p__Hydrogenedentota_7
## 8      Ga0485172_metabat2_ours.152   p__Actinobacteriota_8
## 9  Ga0485161_metabat2_ours.019_sub  p__Verrucomicrobiota_9
## 10 Ga0485168_metabat2_ours.050_sub  p__Actinobacteriota_10
## 11     Ga0485157_metabat2_ours.077  p__Campylobacterota_11
## 12      Ga0485169_metabat1.187_sub p__Verrucomicrobiota_12
## 13     Ga0485169_metabat2_ours.242 p__Verrucomicrobiota_13
## 14          Ga0485160_metabat1.086     p__Cyanobacteria_14
## 15        Ga0485163_maxbin.183_sub p__Verrucomicrobiota_15

Interpretation

Analysis 11

This analysis focuses on the genome p__Bacteroidota_6(Ga0485171_metabat1.063), a significant entity within our microbial network due to its degree centrality. Highlighting its extensive connections within the network, we undertake a permutation analysis where p__Bacteroidota_6 is swapped with 14 other randomly selected OTUs. This process aims to examine the impact of p__Bacteroidota_6 on the network’s structure and functionality by observing how the network adapts to the reassignment of this highly connected genome.

# Proceed with the rest of the script
data <- read_csv("Fw_ lake mendota data/coverm_431_MAGS_metagenomes_reads_count.csv")

## Rows: 431 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Genome
## dbl (16): 2020-10-19_23.5m, 2020-10-08_15m, 2020-10-19_15m, 2020-09-11_15m, ...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

data_t <- t(data)
data_df <- as.data.frame(data_t)
colnames(data_df) <- data_df[1, ]
data_df <- data_df[-1, ]

excluded_columns <- c("Ga0485158_metabat2_ours.098",
"Ga0485159_metabat2_ours.079",
"Ga0485171_metabat2_ours.127_sub",
"Ga0485171_metabat2_ours.004",
"Ga0485170_maxbin.090",
"Ga0485171_metabat1.063",
"Ga0485157_metabat2_ours.019",
"Ga0485166_metabat2_ours.038",
"Ga0485167_metabat2_ours.023",
"Ga0485170_maxbin.059_sub",
"Ga0485171_maxbin.130_sub",
"Ga0485160_metabat2_ours.158_sub",
"Ga0485161_maxbin.110",
"Ga0485161_metabat1.096",
"Ga0485161_metabat2_ours.167_sub")

set.seed(42)
available_columns <- setdiff(colnames(data_df), excluded_columns)
random_column_names <- sample(available_columns, 14)
#print(random_column_names)
taxonomy_file_path <- 'Fw_ lake mendota data/MAG_taxonomy.tsv'
taxonomy_df <- read_tsv(taxonomy_file_path)

## Rows: 431 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (8): Genome, Domain, Phylum, Class, Order, Family, Genus, Species
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

t_count_file_path <- 't_count_columnC.csv'
t_count_df <- read_csv(t_count_file_path)

## Rows: 16 Columns: 442
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (1): Sample
## dbl (441): Ga0485157_maxbin.014, Ga0485157_maxbin.074_sub, Ga0485157_maxbin....
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Create a mapping of genomes to phylum
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)

genomes_list <- c(
  "Ga0485159_maxbin.004_sub","Ga0485169_maxbin.153","Ga0485163_maxbin.002_sub","Ga0485159_metabat2_ours.130_sub","Ga0485164_metabat1.042_sub","Ga0485171_metabat1.063","Ga0485162_metabat2_ours.088" ,"Ga0485161_maxbin.064","Ga0485172_metabat2_ours.152" ,"Ga0485161_metabat2_jgi.003_sub","Ga0485168_metabat2_ours.010","Ga0485157_metabat2_ours.068_sub","Ga0485169_maxbin.226_sub","Ga0485169_metabat2_ours.154","Ga0485160_maxbin.164_sub"   
)

new_column_names_list <- vector("list", length(genomes_list))
names(new_column_names_list) <- genomes_list

seq_num <- 1

for (genome in genomes_list) {
  phylum <- genome_to_phylum_map[genome]
  
  if (!is.null(phylum) && genome %in% colnames(t_count_df)) {
    # Construct the new column name using the phylum and the current sequence number
    new_column_name <- paste(phylum, seq_num, sep = "_")
    
    # Update the list with the new column name
    new_column_names_list[genome] <- new_column_name
    
    # Rename the column in t_count_df
    colnames(t_count_df)[colnames(t_count_df) == genome] <- new_column_name
    
    # Increment the sequence number for the next iteration
    seq_num <- seq_num + 1
  }
}

# Display the first few rows of the modified DataFrame to verify changes
#print(head(t_count_df))
#print(new_column_names_list)

Figure 11

library(CARlasso)
set.seed(42)
t_count_df$DO_mg_L <- ifelse(t_count_df$DO_mg_L < 0, 0, t_count_df$DO_mg_L)
last_10_cols <- tail(names(t_count_df), 10)
t_count_df <- t_count_df%>%
  mutate(across(all_of(last_10_cols), ~scale(., center = min(.), scale = max(.) - min(.))[,1]))

predictor_formula_part <- paste(new_column_names_list, collapse = " + ")
# Construct the full formula by appending the response variables and predictors
full_formula <- as.formula(paste(predictor_formula_part,"~", "depth + wtemp_in_celsius + specific_conductivity + chlorophyll_RFU + phycocyanin_RFU + Dissolved_organic_matter_RFU + Turbidity_RFU + DO_sat_perc + DO_mg_L + PH "))
 otu_res <- CARlasso(full_formula, data = t_count_df, adaptive = TRUE, link="log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

  otu_res <- horseshoe(otu_res)
 plot(otu_res)

 phylum_levels_vector <- unlist(new_column_names_list)

# Create the reference table with genomes_list and the flattened phylum_levels_vector
reference_table <- data.frame(
  Original_Genome = names(phylum_levels_vector),  
  Phylum_Levels = phylum_levels_vector,
  stringsAsFactors = FALSE,  # Ensuring character data does not convert to factors
  row.names = NULL 
)

Table 11

print(reference_table)

##                    Original_Genome           Phylum_Levels
## 1         Ga0485159_maxbin.004_sub      p__Cyanobacteria_1
## 2             Ga0485169_maxbin.153     p__Proteobacteria_2
## 3         Ga0485163_maxbin.002_sub    p__Planctomycetota_3
## 4  Ga0485159_metabat2_ours.130_sub       p__Bacteroidota_4
## 5       Ga0485164_metabat1.042_sub     p__Proteobacteria_5
## 6           Ga0485171_metabat1.063       p__Bacteroidota_6
## 7      Ga0485162_metabat2_ours.088   p__Actinobacteriota_7
## 8             Ga0485161_maxbin.064   p__Actinobacteriota_8
## 9      Ga0485172_metabat2_ours.152   p__Actinobacteriota_9
## 10  Ga0485161_metabat2_jgi.003_sub p__Verrucomicrobiota_10
## 11     Ga0485168_metabat2_ours.010    p__Proteobacteria_11
## 12 Ga0485157_metabat2_ours.068_sub      p__Bacteroidota_12
## 13        Ga0485169_maxbin.226_sub p__Verrucomicrobiota_13
## 14     Ga0485169_metabat2_ours.154      p__Firmicutes_A_14
## 15        Ga0485160_maxbin.164_sub      p__Bacteroidota_15

Interpretation

After permuting genome Ga0485171_metabat1.063(p__Bacteroidota_6) with 14 other random OTUs, we note a significant change: its previously strong connections with various environmental features, observed in Analysis 6, have dissipated. This shift highlights the community-dependent nature of p__Bacteroidota_6’s role and underscores the dynamic adaptability of microbial networks to changes in their composition.

Analysis 12

In this expanded analysis, we continue to focus on genome Ga0485171_metabat1.063(p__Bacteroidota_6), recognized for its substantial network connections. This iteration involves permuting p__Bacteroidota_6 alongside 14 other randomly selected OTUs across 100 random network configurations. The objective is to quantitatively assess the significance of p__Bacteroidota_6 within these varied network structures by measuring how often, within these 100 permutations, the genome emerges as important. Specifically, this OTU is deemed important if its edge value falls above the 90th percentile in the distribution of all edge values within the network. This systematic repetition provides a robust statistical framework to evaluate the resilience of p__Bacteroidota_6’s network influence and its ecological role across multiple hypothetical community compositions. The outcome, reported as a percentage, will highlight the frequency at which p__Bacteroidota_6 retains its central importance, offering deeper insights into its consistency as a key connector within the microbial community under diverse structural scenarios.

library(readr)
library(CARlasso)

# Assuming initial data loading and transformation is done
data <- read_csv("Fw_ lake mendota data/coverm_431_MAGS_metagenomes_reads_count.csv")

## Rows: 431 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Genome
## dbl (16): 2020-10-19_23.5m, 2020-10-08_15m, 2020-10-19_15m, 2020-09-11_15m, ...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

data_t <- t(data)
data_df <- as.data.frame(data_t)
colnames(data_df) <- data_df[1, ]
data_df <- data_df[-1, ]

# Load the taxonomy and T-count files
taxonomy_df <- read_tsv('Fw_ lake mendota data/MAG_taxonomy.tsv')

## Rows: 431 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (8): Genome, Domain, Phylum, Class, Order, Family, Genus, Species
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

t_count_df <- read_csv('t_count_columnC.csv')

## Rows: 16 Columns: 442
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (1): Sample
## dbl (441): Ga0485157_maxbin.014, Ga0485157_maxbin.074_sub, Ga0485157_maxbin....
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Create a mapping of genomes to phylum
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)

excluded_columns <- c(
  "Ga0485158_metabat2_ours.098",
  "Ga0485159_metabat2_ours.079",
  "Ga0485171_metabat2_ours.127_sub",
  "Ga0485171_metabat2_ours.004",
  "Ga0485170_maxbin.090",
  "Ga0485171_metabat1.063",
  "Ga0485157_metabat2_ours.019",
  "Ga0485166_metabat2_ours.038",
  "Ga0485167_metabat2_ours.023",
  "Ga0485170_maxbin.059_sub",
  "Ga0485171_maxbin.130_sub",
  "Ga0485160_metabat2_ours.158_sub",
  "Ga0485161_maxbin.110",
  "Ga0485161_metabat1.096",
  "Ga0485161_metabat2_ours.167_sub",
  'Ga0485157_metabat2_jgi.016',
 'Ga0485163_metabat1.131',
 'Ga0485161_metabat2_jgi.016',
 'Ga0485161_metabat2_ours.188_sub',
 'Ga0485158_metabat1.076',
 'Ga0485167_maxbin.132',
 'Ga0485161_metabat2_jgi.003_sub',
 'Ga0485167_metabat2_ours.110_sub',
 'Ga0485169_metabat2_ours.047_sub',
 'Ga0485167_metabat2_ours.008',
 'Ga0485172_maxbin.051_sub',
 'Ga0485172_maxbin.047_sub',
 'Ga0485168_metabat2_ours.001_sub',
 'Ga0485163_metabat2_ours.198',
 'Ga0485170_metabat2_ours.102',
 'Ga0485169_maxbin.156',
 'Ga0485159_maxbin.127_sub',
 'Ga0485159_metabat2_jgi.002',
 'Ga0485160_metabat2_jgi.018',
 'Ga0485166_maxbin.099',
 'Ga0485163_metabat2_jgi.007',
 'Ga0485160_maxbin.046',
 'Ga0485163_maxbin.058_sub',
 'Ga0485164_metabat1.042_sub',
 'Ga0485163_maxbin.075_sub',
 'Ga0485162_metabat2_ours.050'
)

available_columns <- setdiff(colnames(data_df), excluded_columns)

#set.seed(42) # For reproducibility

# Function to update t_count_df based on sampled genomes
update_t_count_df <- function(sampled_genomes, t_count_df, genome_to_phylum_map) {
  updated_column_names <- vector("character", length(sampled_genomes))
  
  for (i in seq_along(sampled_genomes)) {
    genome <- sampled_genomes[i]
    phylum <- genome_to_phylum_map[genome]
    if (!is.na(phylum)) {
      new_column_name <- paste(phylum, i, sep = "_")
      updated_column_names[i] <- new_column_name
      if (genome %in% colnames(t_count_df)) {
        colnames(t_count_df)[colnames(t_count_df) == genome] <- new_column_name
      }
    } else {
      updated_column_names[i] <- genome # Use original name if no mapping found
    }
  }
  
  return(list(updated_df = t_count_df, selected_mags = updated_column_names))
}

results_90percent <- list()

# Initialize counters
count_values_abs_greater_than_10_in_col6 <- 0
count_values_abs_greater_than_10_in_rows_8_and_9_col6 <- 0

base_seed <- 42

for (i in 1:100) {
  set.seed(base_seed + i)
  sampled_columns <- sample(available_columns, 5)
  additional_columns <- sample(setdiff(available_columns, sampled_columns), 9)
  sampled_genomes <- c(sampled_columns, "Ga0485171_metabat1.063", additional_columns)
  
  list_results <- update_t_count_df(sampled_genomes, t_count_df, genome_to_phylum_map)
  updated_t_count_df <- list_results$updated_df
  new_column_names_list <- list_results$selected_mags
  
  changed_col <- updated_t_count_df
  
  # Replace negative DO_mg_L values with 0
  changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
  
  # Get the names of the last 10 columns
  last_10_cols <- tail(names(changed_col), 10)
  
  # Apply min-max scaling to the last 10 columns
  changed_col <- changed_col %>%
    mutate(across(all_of(last_10_cols), ~ ( . - min(.)) / (max(.) - min(.)) ))
  
  # Construct the predictor formula part with the updated column names
  predictor_formula_part <- paste(new_column_names_list, collapse = " + ")
  
  full_formula <- as.formula(paste(predictor_formula_part,"~", "depth + wtemp_in_celsius + specific_conductivity + chlorophyll_RFU + phycocyanin_RFU + Dissolved_organic_matter_RFU + Turbidity_RFU + DO_sat_perc + DO_mg_L + PH "))
  
  # Using tryCatch to handle potential errors in CARlasso
  otu_res <- tryCatch({
    set.seed(42)
    CARlasso(full_formula, data = changed_col, adaptive = TRUE, link = "log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)
  }, error = function(e) {
    # If an error occurs, return NULL and proceed to the next iteration
    NULL
  })
  
  # Check if CARlasso ran successfully
  if (is.null(otu_res)) {
    # Skip the rest of this iteration if CARlasso failed
    next
  }
  
  # Apply horseshoe transformation
  #otu_res_hs <- horseshoe(otu_res)
  
  # Assuming otu_res$point_est$CAR$B is your matrix
  data_matrix <- otu_res$point_est$CAR$B

# Convert the matrix elements to their absolute values
  data_matrix_abs <- abs(data_matrix)

# Convert the absolute value matrix to a vector
  data_vector <- as.vector(data_matrix_abs)

# Calculate the 90th percentile of the absolute values
  ninety_percentile <- quantile(data_vector, 0.9)
  
  # Check and count if any absolute value in column 6
  if (any(abs(otu_res$point_est$CAR$B[, 6]) > ninety_percentile)) {
    count_values_abs_greater_than_10_in_col6 <- count_values_abs_greater_than_10_in_col6 + 1
  }

  # Check and count if absolute values in rows 8 and 9 of column 6 
  if (any(abs(otu_res$point_est$CAR$B[c(1:5, 8:9), 6]) > ninety_percentile)) {
    count_values_abs_greater_than_10_in_rows_8_and_9_col6 <- count_values_abs_greater_than_10_in_rows_8_and_9_col6 + 1
  }

  # Store the horseshoe analysis results
  results_90percent[[i]] <- ninety_percentile
}

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

# Calculate percentages
percentage_col14 <- (count_values_abs_greater_than_10_in_col6 / sum(!sapply(results_90percent, is.null))) * 100
percentage_rows_8_and_9_col6 <- (count_values_abs_greater_than_10_in_rows_8_and_9_col6/ sum(!sapply(results_90percent, is.null))) * 100

Value of percenatge

cat("Percentage of iterations where abs value is upon the 90 pecent quantile is:", percentage_rows_8_and_9_col6, "%\n")

## Percentage of iterations where abs value is upon the 90 pecent quantile is: 53.68421 %

Interpretation

Analysis 13

In this phase of our study, We aim to assess the significance of Genome p__Desulfobacterota_15(Ga0485162_metabat1.001) across 100 random microbial networks by permuting it with 14 other OTUs. Significance is determined if its connectivity exceeds the 90th percentile in edge values, quantifying its robustness as a key connector.

library(readr)
library(CARlasso)

# Assuming initial data loading and transformation is done
data <- read_csv("Fw_ lake mendota data/coverm_431_MAGS_metagenomes_reads_count.csv")

## Rows: 431 Columns: 17
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): Genome
## dbl (16): 2020-10-19_23.5m, 2020-10-08_15m, 2020-10-19_15m, 2020-09-11_15m, ...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

data_t <- t(data)
data_df <- as.data.frame(data_t)
colnames(data_df) <- data_df[1, ]
data_df <- data_df[-1, ]

# Load the taxonomy and T-count files
taxonomy_df <- read_tsv('Fw_ lake mendota data/MAG_taxonomy.tsv')

## Rows: 431 Columns: 8
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (8): Genome, Domain, Phylum, Class, Order, Family, Genus, Species
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

t_count_df <- read_csv('t_count_columnC.csv')

## Rows: 16 Columns: 442
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr   (1): Sample
## dbl (441): Ga0485157_maxbin.014, Ga0485157_maxbin.074_sub, Ga0485157_maxbin....
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# Create a mapping of genomes to phylum
genome_to_phylum_map <- setNames(taxonomy_df$Phylum, taxonomy_df$Genome)

excluded_columns <- c(
  'Ga0485157_metabat1.059',
    'Ga0485167_maxbin.109',
    'Ga0485162_maxbin.089',
    'Ga0485161_maxbin.110',
    'Ga0485161_maxbin.075',
    'Ga0485157_metabat1.036',
    'Ga0485165_metabat2_ours.012_sub',
    'Ga0485169_maxbin.201_sub',
    'Ga0485172_maxbin.081_sub',
    'Ga0485168_maxbin.153',
    'Ga0485172_metabat2_ours.083',
    'Ga0485162_maxbin.023',
    'Ga0485160_maxbin.092',
    'Ga0485158_metabat2_jgi.024',
    'Ga0485162_metabat1.001',
  'Ga0485157_metabat2_jgi.016',
 'Ga0485163_metabat1.131',
 'Ga0485161_metabat2_jgi.016',
 'Ga0485161_metabat2_ours.188_sub',
 'Ga0485158_metabat1.076',
 'Ga0485167_maxbin.132',
 'Ga0485161_metabat2_jgi.003_sub',
 'Ga0485167_metabat2_ours.110_sub',
 'Ga0485169_metabat2_ours.047_sub',
 'Ga0485167_metabat2_ours.008',
 'Ga0485172_maxbin.051_sub',
 'Ga0485172_maxbin.047_sub',
 'Ga0485168_metabat2_ours.001_sub',
 'Ga0485163_metabat2_ours.198',
 'Ga0485170_metabat2_ours.102',
 'Ga0485169_maxbin.156',
 'Ga0485159_maxbin.127_sub',
 'Ga0485159_metabat2_jgi.002',
 'Ga0485160_metabat2_jgi.018',
 'Ga0485166_maxbin.099',
 'Ga0485163_metabat2_jgi.007',
 'Ga0485160_maxbin.046',
 'Ga0485163_maxbin.058_sub',
 'Ga0485164_metabat1.042_sub',
 'Ga0485163_maxbin.075_sub',
 'Ga0485162_metabat2_ours.050'
)

available_columns <- setdiff(colnames(data_df), excluded_columns)

#set.seed(42) # For reproducibility

# Function to update t_count_df based on sampled genomes
update_t_count_df <- function(sampled_genomes, t_count_df, genome_to_phylum_map) {
  updated_column_names <- vector("character", length(sampled_genomes))
  
  for (i in seq_along(sampled_genomes)) {
    genome <- sampled_genomes[i]
    phylum <- genome_to_phylum_map[genome]
    if (!is.na(phylum)) {
      new_column_name <- paste(phylum, i, sep = "_")
      updated_column_names[i] <- new_column_name
      if (genome %in% colnames(t_count_df)) {
        colnames(t_count_df)[colnames(t_count_df) == genome] <- new_column_name
      }
    } else {
      updated_column_names[i] <- genome # Use original name if no mapping found
    }
  }
  
  return(list(updated_df = t_count_df, selected_mags = updated_column_names))
}

results_90percent <- list()

# Initialize counters
count_values_abs_greater_than_10_in_col4 <- 0
count_values_abs_greater_than_10_in_rows_8_and_9_col4 <- 0

base_seed <- 42

for (i in 1:100) {
  set.seed(base_seed + i)
  sampled_columns <- sample(available_columns, 14)
  #additional_columns <- sample(setdiff(available_columns, sampled_columns), 11)
  sampled_genomes <- c(sampled_columns, "Ga0485162_metabat1.001")
  
  list_results <- update_t_count_df(sampled_genomes, t_count_df, genome_to_phylum_map)
  updated_t_count_df <- list_results$updated_df
  new_column_names_list <- list_results$selected_mags
  
  changed_col <- updated_t_count_df
  
  # Replace negative DO_mg_L values with 0
  changed_col$DO_mg_L <- ifelse(changed_col$DO_mg_L < 0, 0, changed_col$DO_mg_L)
  
  # Get the names of the last 10 columns
  last_10_cols <- tail(names(changed_col), 10)
  
  # Apply min-max scaling to the last 10 columns
  changed_col <- changed_col %>%
    mutate(across(all_of(last_10_cols), ~ ( . - min(.)) / (max(.) - min(.)) ))
  
  # Construct the predictor formula part with the updated column names
  predictor_formula_part <- paste(new_column_names_list, collapse = " + ")
  
  full_formula <- as.formula(paste(predictor_formula_part,"~", "depth + wtemp_in_celsius + specific_conductivity + chlorophyll_RFU + phycocyanin_RFU + Dissolved_organic_matter_RFU + Turbidity_RFU + DO_sat_perc + DO_mg_L + PH "))
  
  # Using tryCatch to handle potential errors in CARlasso
  otu_res <- tryCatch({
    set.seed(42)
    CARlasso(full_formula, data = changed_col, adaptive = TRUE, link = "log", n_iter = 5000, n_burn_in = 1000, thin_by = 10)
  }, error = function(e) {
    # If an error occurs, return NULL and proceed to the next iteration
    NULL
  })
  
  # Check if CARlasso ran successfully
  if (is.null(otu_res)) {
    # Skip the rest of this iteration if CARlasso failed
    next
  }
  
  # Apply horseshoe transformation
  #otu_res_hs <- horseshoe(otu_res)
  
  # Assuming otu_res$point_est$CAR$B is your matrix
  data_matrix <- otu_res$point_est$CAR$B

# Convert the matrix elements to their absolute values
  data_matrix_abs <- abs(data_matrix)

# Convert the absolute value matrix to a vector
  data_vector <- as.vector(data_matrix_abs)

# Calculate the 90th percentile of the absolute values
  ninety_percentile_15 <- quantile(data_vector, 0.9)
  
  # Check and count if any absolute value in column 15
  if (any(abs(otu_res$point_est$CAR$B[, 15]) > ninety_percentile_15)) {
    count_values_abs_greater_than_10_in_col4 <- count_values_abs_greater_than_10_in_col4 + 1
  }

  # Check and count if absolute values in rows 5 and 6 of column 15
  if (any(abs(otu_res$point_est$CAR$B[5:6, 15]) > ninety_percentile_15)) {
    count_values_abs_greater_than_10_in_rows_8_and_9_col4 <- count_values_abs_greater_than_10_in_rows_8_and_9_col4 + 1
  }

  # Store the horseshoe analysis results
  results_90percent[[i]] <- ninety_percentile_15
}

## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done
## 
## Predictors will be centered.
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for beta 
## 
## Algorithm set to be adapive. Assuming all hyper parameters are the same for Omega's off diagonal entries 
## 
## Algorithm set to be adaptive. Assuming priors are all the same for Omega's diagonals 
## 
## Algorithm start...
## 
## progress:
## 
## 
## done

percentage_col4 <- (count_values_abs_greater_than_10_in_col4 / sum(!sapply(results_90percent, is.null))) * 100
percentage_rows_8_and_9_col4 <- (count_values_abs_greater_than_10_in_rows_8_and_9_col4 / sum(!sapply(results_90percent, is.null))) * 100

# Print results
#cat("Percentage of iterations where any abs value > 10 in col 14:", percentage_col14, "%\n")
#cat("Percentage of iterations where abs value is upon the 90 pecent quantile is:", percentage_rows_8_and_9_col4, "%\n")

Value of percenatge

cat("Percentage of iterations where abs value is upon the 90 pecent quantile is:", percentage_rows_8_and_9_col4, "%\n")

## Percentage of iterations where abs value is upon the 90 pecent quantile is: 25.7732 %

Interpretation